Two problems involving high-resolution reconstruction from nonuniformly sampled data in x-ray computed tomography are addressed. A technique based on the theorem for sampling on unions of shifted lattices is introduced which exploits the symmetry property in two-dimensional fan beam computed tomography and permits the reconstruction of images with twice the...
X-ray computed tomography is a noninvasive imaging modality capable of reconstructing exact density values of 3D objects. Computed tomography machines are deployed across the world to provide doctors with an image that reveals more detail than a standard x-ray image. We investigate algorithms based on exact computed tomography reconstruction formulas...
In this thesis, we will study certain generalizations of the classical Shannon Sampling Theorem, which allows for the reconstruction of a pi-band-limited, square-integrable function from its samples on the integers. J. R. Higgins provided a generalization where the integers can be perturbed by less than 1/4, which includes nonuniform and...
Sampling theorems provide exact interpolation formulas for bandlimited
functions. They play a fundamental role in signal processing. A function is called
bandlimited if its Fourier transform vanishes outside a compact set. A generalized
sampling theorem in the framework of locally compact Abelian groups is presented.
Sampling sets are finite unions...
We explore two characteristic features of x-ray computed tomography inversion formulas in two and
three dimensions that are dependent on π-lines. In such formulas the data from a given source
position contribute only to the reconstruction of ƒ(x) for x in a certain region, called the region
of backprojection. The...
In this paper, we provide a thorough proof of most of Bertrand's Theorem. Using Arnold's book "Mathematical methods of classical mechanics" as a backbone and calculus methods demonstrated by Jovanović in his article "A note on the proof of Bertrand's theorem," we show that for masses in a central field...
Facial recognition has become increasingly important in recent years, due to the wide range of applications it has in fields such as security, surveillance, and human-computer interaction. Three popular methods for facial recognition are the Principal Component Analysis (PCA), Karhunen-Loeve Expansions, which is fundamentally a continuous form of PCA but...
In this paper, we discuss two possible modifications to a numerical solution method for a model of microbiologically induced calcite precipitation (MICP). MICP provides a means to seal cracks in the surfaces of geological structures. From a mathematical and computational point of view MICP has very interesting features which make...
In previous papers by Awrejcewicz in 1986 and Narayanan and Jayaraman in 1991, it was claimed that the nonlinear oscillator with dry friction exhibited chaos for several forcing frequencies. The chaos determination was achieved using the characteristic exponent of Lyapunov which requires the right-hand side of the differential equation to...
